Class 7 Math: Real Numbers
By Pratap Sanjay Sir
Introduction to Real Numbers
Real numbers include all numbers on the number line, both rational and irrational. They are fundamental in mathematics and used in everyday calculations and scientific measurements.
Definitions
Real Numbers: Numbers that can be found on the number line, including rational and irrational numbers.
Rational Numbers: Numbers that can be expressed as a fraction of two integers.
Irrational Numbers: Numbers that cannot be expressed as a simple fraction.
Integers: Whole numbers and their negatives.
Prime Numbers: Numbers with only two divisors: 1 and themselves.
Composite Numbers: Numbers with more than two divisors.
Properties of Real Numbers
Real numbers have several important properties:
- Closure: The sum or product of any two real numbers is a real number.
- Commutative Property: a + b = b + a and ab = ba for any real numbers a and b.
- Associative Property: (a + b) + c = a + (b + c) and (ab)c = a(bc) for any real numbers a, b, and c.
- Distributive Property: a(b + c) = ab + ac for any real numbers a, b, and c.
- Identity Property: There exists an additive identity (0) and a multiplicative identity (1).
- Inverse Property: Every real number a has an additive inverse (-a) and a multiplicative inverse (1/a, a ≠ 0).
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